Abstract. We prove First Fundamental Theorems of Coinvariant Theory for th*
*e standard
coactions of the quantum groups Oq(GLt(K)) and Oq(SLt(K)) on the quantized*
* algebra
Oq(Mm,t(K)) Oq(Mt,n(K)). (Here K is an arbitrary field and q an arbitra*
*ry nonzero
scalar.) In both cases, the set of coinvariants is a subalgebra of Oq(Mm,t*